Two blocks of masses 2 kg and 3 kg are connected by a light string over a frictionless pulley. If the 3 kg block is hanging, what is the acceleration of the system?
Practice Questions
1 question
Q1
Two blocks of masses 2 kg and 3 kg are connected by a light string over a frictionless pulley. If the 3 kg block is hanging, what is the acceleration of the system?
1.2 m/s²
2 m/s²
3 m/s²
4 m/s²
Using Newton's second law, the net force is (3 kg * 9.8 m/s²) - (2 kg * a) = (2 kg + 3 kg) * a. Solving gives a = 1.2 m/s².
Questions & Step-by-step Solutions
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Q
Q: Two blocks of masses 2 kg and 3 kg are connected by a light string over a frictionless pulley. If the 3 kg block is hanging, what is the acceleration of the system?
Solution: Using Newton's second law, the net force is (3 kg * 9.8 m/s²) - (2 kg * a) = (2 kg + 3 kg) * a. Solving gives a = 1.2 m/s².
Steps: 12
Step 1: Identify the masses of the blocks. The first block has a mass of 2 kg and the second block has a mass of 3 kg.
Step 2: Understand that the 3 kg block is hanging and will cause the system to accelerate downwards due to gravity.
Step 3: Calculate the weight of the 3 kg block using the formula: weight = mass * gravity. Here, gravity is approximately 9.8 m/s². So, weight = 3 kg * 9.8 m/s² = 29.4 N.
Step 4: The 2 kg block will experience a force due to the tension in the string. We need to find the net force acting on the system.
Step 5: Write the equation for the net force. The net force is the weight of the 3 kg block minus the force due to the acceleration of the 2 kg block: (3 kg * 9.8 m/s²) - (2 kg * a).
Step 6: The total mass of the system is the sum of both blocks: 2 kg + 3 kg = 5 kg.
Step 7: According to Newton's second law, the net force is also equal to the total mass times the acceleration: (2 kg + 3 kg) * a.
Step 8: Set the two expressions for net force equal to each other: (3 kg * 9.8 m/s²) - (2 kg * a) = (2 kg + 3 kg) * a.
Step 9: Rearrange the equation to solve for acceleration 'a'. This gives: 29.4 N - 2a = 5a.
Step 10: Combine like terms: 29.4 N = 7a.
Step 11: Solve for 'a' by dividing both sides by 7: a = 29.4 N / 7 = 4.2 m/s².
Step 12: The final answer for the acceleration of the system is approximately 4.2 m/s².
